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Magnus C. Ørke: Highest waves for fractional Korteweg–De Vries and Degasperis–Procesi equations

Time: Wed 2023-11-01 10.00 - 11.00

Location: Institut Mittag-Leffler, Seminar Hall Kuskvillan and Zoom

Video link: Meeting ID: 921 756 1880

Participating: Magnus C. Ørke, University of Oslo

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In recent years global bifurcation theory in combination with precise regularity estimates has been used to prove existence of specific classes of traveling wave solutions for nonlinear and nonlocal PDEs. I will discuss this method for a class of fractional Korteweg–De Vries and fractional Degasperis–Procesi equations with an inhomogeneous Fourier multiplier of parametrized order in the range of \((-1, 0)\), and show that there are highest, cusped traveling-wave solutions for both equations, characterized by optimal Hölder regularity exactly attained in the cusp.